
"""simple docstring"""



import math
from enum import Enum
from typing import Optional, Union

from torch.optim import Optimizer
from torch.optim.lr_scheduler import LambdaLR

from .utils import logging


__lowercase						:     Any							      =		logging.get_logger(__name__)





class 					lowerCAmelCase			(				SCREAMING_SNAKE_CASE_					):
     """simple docstring"""







     __lowercase						:Tuple          =    "linear"
     __lowercase						:Optional[int]          =    "cosine"
     __lowercase						:Optional[int]          =    "cosine_with_restarts"
     __lowercase						:List[Any]          =    "polynomial"
     __lowercase						:Any          =    "constant"
     __lowercase						:int          =    "constant_with_warmup"
     __lowercase						:Dict          =    "piecewise_constant"



def lowerCamelCase_				(     _lowerCamelCase			:	Optimizer					,				_lowerCamelCase			:	int = -1				):
       return LambdaLR(_lowerCamelCase					,				lambda _lowerCamelCase				: 1					,				last_epoch=_lowerCamelCase				)


def lowerCamelCase_				(     _lowerCamelCase			:	Optimizer					,				_lowerCamelCase			:	int					,				_lowerCamelCase			:	int = -1				):

       def lr_lambda(_lowerCamelCase			:	int				):
              if current_step < num_warmup_steps:
                     return float(_lowerCamelCase				) / float(max(1.0					,				_lowerCamelCase				)				)
              return 1.0

       return LambdaLR(_lowerCamelCase					,				_lowerCamelCase					,				last_epoch=_lowerCamelCase				)


def lowerCamelCase_				(     _lowerCamelCase			:	Optimizer					,				_lowerCamelCase			:	str					,				_lowerCamelCase			:	int = -1				):
       lowerCamelCase_       							=		{}
       lowerCamelCase_       							=		step_rules.split(''','''				)
       for rule_str in rule_list[:-1]:
              lowerCamelCase_							,							lowerCamelCase_       							=		rule_str.split(''':'''				)
              lowerCamelCase_       							=		int(_lowerCamelCase				)
              lowerCamelCase_       							=		float(_lowerCamelCase				)
              lowerCamelCase_       							=		value
       lowerCamelCase_       							=		float(rule_list[-1]				)

       def create_rules_function(_lowerCamelCase			:	List[Any]					,				_lowerCamelCase			:	Optional[int]				):
              def rule_func(_lowerCamelCase			:	int				) -> float:
                     lowerCamelCase_       							=		sorted(rules_dict.keys()				)
                     for i, sorted_step in enumerate(_lowerCamelCase				):
                            if steps < sorted_step:
                                   return rules_dict[sorted_steps[i]]
                     return last_lr_multiple

              return rule_func

       lowerCamelCase_       							=		create_rules_function(_lowerCamelCase					,				_lowerCamelCase				)

       return LambdaLR(_lowerCamelCase					,				_lowerCamelCase					,				last_epoch=_lowerCamelCase				)


def lowerCamelCase_				(     _lowerCamelCase			:	Union[str, Any]					,				_lowerCamelCase			:	List[Any]					,				_lowerCamelCase			:	Union[str, Any]					,				_lowerCamelCase			:	List[str]=-1				):

       def lr_lambda(_lowerCamelCase			:	int				):
              if current_step < num_warmup_steps:
                     return float(_lowerCamelCase				) / float(max(1					,				_lowerCamelCase				)				)
              return max(
                  0.0					,				float(num_training_steps - current_step				) / float(max(1					,				num_training_steps - num_warmup_steps				)				)				)

       return LambdaLR(_lowerCamelCase					,				_lowerCamelCase					,				_lowerCamelCase				)


def lowerCamelCase_				(     _lowerCamelCase			:	Optimizer					,				_lowerCamelCase			:	int					,				_lowerCamelCase			:	int					,				_lowerCamelCase			:	float = 0.5					,				_lowerCamelCase			:	int = -1				):

       def lr_lambda(_lowerCamelCase			:	Union[str, Any]				):
              if current_step < num_warmup_steps:
                     return float(_lowerCamelCase				) / float(max(1					,				_lowerCamelCase				)				)
              lowerCamelCase_       							=		float(current_step - num_warmup_steps				) / float(max(1					,				num_training_steps - num_warmup_steps				)				)
              return max(0.0					,				0.5 * (1.0 + math.cos(math.pi * float(_lowerCamelCase				) * 2.0 * progress				))				)

       return LambdaLR(_lowerCamelCase					,				_lowerCamelCase					,				_lowerCamelCase				)


def lowerCamelCase_				(     _lowerCamelCase			:	Optimizer					,				_lowerCamelCase			:	int					,				_lowerCamelCase			:	int					,				_lowerCamelCase			:	int = 1					,				_lowerCamelCase			:	int = -1				):

       def lr_lambda(_lowerCamelCase			:	Any				):
              if current_step < num_warmup_steps:
                     return float(_lowerCamelCase				) / float(max(1					,				_lowerCamelCase				)				)
              lowerCamelCase_       							=		float(current_step - num_warmup_steps				) / float(max(1					,				num_training_steps - num_warmup_steps				)				)
              if progress >= 1.0:
                     return 0.0
              return max(0.0					,				0.5 * (1.0 + math.cos(math.pi * ((float(_lowerCamelCase				) * progress) % 1.0)				))				)

       return LambdaLR(_lowerCamelCase					,				_lowerCamelCase					,				_lowerCamelCase				)


def lowerCamelCase_				(     _lowerCamelCase			:	str					,				_lowerCamelCase			:	Optional[int]					,				_lowerCamelCase			:	int					,				_lowerCamelCase			:	Optional[int]=1E-7					,				_lowerCamelCase			:	Optional[int]=1.0					,				_lowerCamelCase			:	int=-1				):
       lowerCamelCase_       							=		optimizer.defaults['''lr''']
       if not (lr_init > lr_end):
              raise ValueError(F"""lr_end ({lr_end}) must be be smaller than initial lr ({lr_init})"""				)

       def lr_lambda(_lowerCamelCase			:	int				):
              if current_step < num_warmup_steps:
                     return float(_lowerCamelCase				) / float(max(1					,				_lowerCamelCase				)				)
              elif current_step > num_training_steps:
                     return lr_end / lr_init  # as LambdaLR multiplies by lr_init
              else:
                     lowerCamelCase_       							=		lr_init - lr_end
                     lowerCamelCase_       							=		num_training_steps - num_warmup_steps
                     lowerCamelCase_       							=		1 - (current_step - num_warmup_steps) / decay_steps
                     lowerCamelCase_       							=		lr_range * pct_remaining**power + lr_end
                     return decay / lr_init  # as LambdaLR multiplies by lr_init

       return LambdaLR(_lowerCamelCase					,				_lowerCamelCase					,				_lowerCamelCase				)


__lowercase						:     int							      =		{
    SchedulerType.LINEAR: get_linear_schedule_with_warmup,
    SchedulerType.COSINE: get_cosine_schedule_with_warmup,
    SchedulerType.COSINE_WITH_RESTARTS: get_cosine_with_hard_restarts_schedule_with_warmup,
    SchedulerType.POLYNOMIAL: get_polynomial_decay_schedule_with_warmup,
    SchedulerType.CONSTANT: get_constant_schedule,
    SchedulerType.CONSTANT_WITH_WARMUP: get_constant_schedule_with_warmup,
    SchedulerType.PIECEWISE_CONSTANT: get_piecewise_constant_schedule,
}





def lowerCamelCase_				(     _lowerCamelCase			:	Union[str, SchedulerType]					,				_lowerCamelCase			:	Optimizer					,				_lowerCamelCase			:	Optional[str] = None					,				_lowerCamelCase			:	Optional[int] = None					,				_lowerCamelCase			:	Optional[int] = None					,				_lowerCamelCase			:	int = 1					,				_lowerCamelCase			:	float = 1.0					,				_lowerCamelCase			:	int = -1					,				):
       lowerCamelCase_       							=		SchedulerType(_lowerCamelCase				)
       lowerCamelCase_       							=		TYPE_TO_SCHEDULER_FUNCTION[name]
       if name == SchedulerType.CONSTANT:
              return schedule_func(_lowerCamelCase					,				last_epoch=_lowerCamelCase				)

       if name == SchedulerType.PIECEWISE_CONSTANT:
              return schedule_func(_lowerCamelCase					,				step_rules=_lowerCamelCase					,				last_epoch=_lowerCamelCase				)

       # All other schedulers require `num_warmup_steps`
       if num_warmup_steps is None:
              raise ValueError(F"""{name} requires `num_warmup_steps`, please provide that argument."""				)

       if name == SchedulerType.CONSTANT_WITH_WARMUP:
              return schedule_func(_lowerCamelCase					,				num_warmup_steps=_lowerCamelCase					,				last_epoch=_lowerCamelCase				)

       # All other schedulers require `num_training_steps`
       if num_training_steps is None:
              raise ValueError(F"""{name} requires `num_training_steps`, please provide that argument."""				)

       if name == SchedulerType.COSINE_WITH_RESTARTS:
              return schedule_func(
                  _lowerCamelCase					,				num_warmup_steps=_lowerCamelCase					,				num_training_steps=_lowerCamelCase					,				num_cycles=_lowerCamelCase					,				last_epoch=_lowerCamelCase					,				)

       if name == SchedulerType.POLYNOMIAL:
              return schedule_func(
                  _lowerCamelCase					,				num_warmup_steps=_lowerCamelCase					,				num_training_steps=_lowerCamelCase					,				power=_lowerCamelCase					,				last_epoch=_lowerCamelCase					,				)

       return schedule_func(
           _lowerCamelCase					,				num_warmup_steps=_lowerCamelCase					,				num_training_steps=_lowerCamelCase					,				last_epoch=_lowerCamelCase				)
def 	lowerCamelCase					(	UpperCamelCase     :				int = 60_08_51_47_51_43							)   ->    int:

		try:
				_lowerCamelCase				   =  int(UpperCamelCase							)
		except (TypeError, ValueError):
				raise TypeError('Parameter n must be int or castable to int.'							)
		if n <= 0:
				raise ValueError('Parameter n must be greater than or equal to one.'							)
		_lowerCamelCase				   =  1
		_lowerCamelCase				   =  2
		while i * i <= n:
				while n % i == 0:
						_lowerCamelCase				   =  i
						n //= i
				i += 1
		if n > 1:
				_lowerCamelCase				   =  n
		return int(UpperCamelCase							)


if __name__ == "__main__":
				print(F'''{solution() = }''')